When does one care about the units of torque? When one buys a torque wrench. A quick market review aka first page of Google results finds the following units in product catalogs (American market, obviously): ft.-lb., ft.-lbs., in./lb., ft./lb., ft./lbs., Nm.

No mention of mN. On the other hand a number of those units are wrong if symbols are taken to have their usual meanings.

So while your teacher certainly has reasons (cross product order as others pointed out) to chose the (ugly, misleading to anyone not using the same textbook) mN over Nm, I believe they would be doing you a better service by preparing you for a world where things don't follow a unique prescription and where even basic mathematical concepts are messed up all the time.

When does one care about the units of torque? When one buys a torque wrench. A quick market review aka first page of Google results finds the following units in product catalogs (American market, obviously): ft.-lb., ft.-lbs., in./lb., ft./lb., ft./lbs., Nm.

No mention of mN. On the other hand a number of those units are wrong if symbols are taken to have their usual meanings.

So while your teacher certainly has reasons (cross product order as others pointed out) to chose the (ugly, misleading to anyone not using the same textbook) mN over Nm, I believe they would be doing you a better service by preparing you for a world where things don't follow a unique prescription and where even basic mathematical concepts are messed up all the time instead of insisting on a rule that doesn't exist outside their textbook.